Introduction to Scientific Computing II - Summer 12

Term

Summer 12

Lecturer

Prof. Dr. Michael Bader

Time and Place

Tuesday 8:30-10:00, lecture room MI 02.07.023
First Lecture: April 17

Audience

Computational Science and Engineering, 2nd semester (Module IN2141)

Tutorials

Wolfgang Eckhardt
lecture room MI 02.07.023, time:
Monday 9:00-9:45,
First Tutorial: April 23

Exam

written exam

Semesterwochenstunden / ECTS Credits

2V + 1Ü / 4 Credits

TUMonline

Scientific Computing II

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Contents

This course provides a deeper knowledge in two important fields of scientific computing:

• solution of large sparse systems of linear equations:
  • Gaussian elemination
  • relaxation methods
  • multigrid methods
  • steepest descent
  • conjugate gradient methods
• molecular dynamics simulations
  • the physical model
  • the mathematical model
  • approximations and discretization
  • implementational aspects
  • parallelisation
  • examples of nanofluidic simulations

The course is conceived for computer scientists, mathematicians, engineers, or natural scientists with already a background in the numerical treatment of (partial) differential equations.

Lecture Notes and Material

lecture	material	tutorial	exercise	matlab
Apr 17	Introduction, Relaxation Methods	Apr 23	Slides	Matlab Code
Apr 24	Multigrid Methods, Animations	Apr 30	Iterative Solvers Homework Sheet	Matlab Code
Mai 1	(holiday - no lecture)	May 7	Solution Homework Exercise	Code Tutorial
May 8	Multigrid Methods (cont.)	May 14	slides Multigrid-Solver	2Grid-Solver
May 15	Multigrid Methods (cont.), Animations	May 21	Multigrid	Multigrid-Solver interpolate_4h.m restrict_4h.m restrict_fw.m Homework-Solution AnisotropicMG
May 22	Slides Two-grid analysis	May 28	- (holiday)	-
May 29	- (holiday)	June 4	-	-
June 5	Steepest Descent and Conjugate Gradient Methods (Maple worksheet quadratic.mw, also as PDF)	June 11	Steepest-Descent/CG	SD/CG

Further Material

Annotated slides for the lecture in summer 2010 /(given by Dr. Tobias Weinzierl) are available from the TeleTeachingTool Lecture Archive

Matlab (together with installation instructions) is available from https://matlab.rbg.tum.de/

Literature

• William L. Briggs, Van Emden Henson, Steve F. McCormick. A Multigrid Tutorial. Second Edition. SIAM. 2000.
• J.R. Shewchuk. An Introduction to the Conjugate Gradient Method Without the Agonizing Pain. Edition 1.25. 1994.
• M. Griebel, S. Knapek, G. Zumbusch, and A. Caglar. Numerische Simulation in der Molekulardynamik. Springer, 2004.
• M. P. Allen and D. J. Tildesley. Computer Simulation of Liquids. Oxford University Press, 2003.
• D. Frenkel and B. Smith. Understanding Molecular Simulation from Algorithms to ASpplications. Academic Press (2nd ed.), 2002.
• R. J. Sadus. Molecular Simulation of Fluids; Theory, Algorithms and Object-Orientation. Elsevier, 1999.
• D. Rapaport. The art of molecular dynamics simulation. Camebridge University Press, 1995.